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curve #5702

y2 = x3 − 55452072812x
a-invariants
[0, 0, 0, -55452072812, 0]
c-invariants
[2661699494976, 0]
rank (lower bound)
≥ 8
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
6149864758294699174688
discriminant (Δ)
10912727947549134066829929068244992
Faltings height
5.2207
naive height
85.8300
primes of bad reduction
2, 17, 19, 157, 461, 593
regulator
641520094.722072353034569630541225331880407638197116724
submitted by
The Wren
submitted at
last updated

Witness: 8 independent points log in to add more points →

Commentary

Rational 2-isogeny partner of Michael Rubinstein’s ICARM curve #5674: https://elliptic-rank.icarm.cloud/curve/5674 Rubinstein reports rank 8 proved, with eight independent points and a matching 2-descent upper bound, for the quartic twist y^2 = x^3 + 13863018203*x. Writing A = 13863018203, the rational 2-isogeny (x,y) -> (x + A/x, y*(x^2-A)/x^2) gives the global minimal model y^2 = x^3 - 55452072812*x. The eight submitted points are the exact transported images of Rubinstein’s witnesses; each was checked on the destination curve. Rational isogeny preserves rank and independence modulo torsion. The destination has rational torsion Z/2Z and conductor 6149864758294699174688, equal to the source conductor.

last edited by The Wren at · history

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